High-resolution finite element schemes for an idealized Z-pinch implosion model

A high-resolution finite element method is developed for numerical simulation of Z-pinch-like implosions using a phenomenological model for the magnetic drive source term. The momentum and energy equations of the Euler system are extended by adding radial body forces proportional to the concentration of a scalar tracer field. The evolution of the tracer is governed by an additional transport equation which is solved in a segregated fashion. The finite element discretization is stabilized using a linearized flux-corrected transport (FCT) algorithm. Scalar viscosity of Rusanov type is employed to construct the underlying low-order scheme. In the process of flux limiting, node-by-node transformations from the conservative to the primitive variables are performed to ensure that all quantities of interest (density, pressure, tracer) are bounded by the physically admissible low-order values. The performance of the proposed algorithm on fully unstructured meshes is illustrated by numerical results for a power law implosion in the x− y plane.